Mask having an arbitrary complex transmission function

Abstract

A mask is provided which has a complex transmission function and which includes a transparent layer and a non-transparent layer. The transparent layer has three types of phase-shifting elements, each imparting a different phase shift relative to the others, with the phase-shifting elements alternating in both x and y dimensions. The non-transparent layer has holes arranged in an approximately equally spaced grid pattern defined by common points in borders of the phase-shifting elements. Centers of at least two holes in the non-transparent layer have different offsets from their corresponding common points. Also provided is a mask blank which includes a transparent layer and a non-transparent layer. The transparent layer has three types of phase-shifting elements, each imparting a different phase shift relative to the others, with the phase-shifting elements alternating in both x and y dimensions.

What is claimed is:  
     
       1. A mask having a complex transmission function, comprising: 
       a transparent layer having three types of phase-shifting elements, each imparting a different phase shift relative to the others, with the phase-shifting elements alternating in both x and y dimensions; and  
       a non-transparent layer having holes arranged in an approximately equally spaced grid pattern defined by common points in borders of the phase-shifting elements,  
       wherein centers of at least two holes in the non-transparent layer have different offsets from their corresponding common points.  
     
     
       2. A mask according to claim  1 , wherein the three types of phase-shifting elements produce phase shifts that are offset from each other by approximately 2Π/3 radians. 
     
     
       3. A mask according to claim  1 , wherein the holes have approximately equal sizes and approximately identical shapes. 
     
     
       4. A mask according to claim  1 , wherein dimensions of the holes are between approximately one-tenth and one-twentieth of spacing between the common points. 
     
     
       5. A mask according to claim  1 , wherein the phase-shifting elements are arranged in rows, wherein the three types are arranged in a repeating 123 pattern in each row, and wherein the repeating 123 patterns in each two adjacent rows are offset by approximately 1.5 phase-shifting elements. 
     
     
       6. A mask having a complex transmission function, comprising: 
       a transparent layer having three types of phase-shifting elements arranged such that points common to borders of all three types form a regularly spaced grid; and  
       a non-transparent layer having holes coinciding with the points on the grid,  
       wherein each type of phase-shifting element imparts a different phase shift relative to the others, and wherein centers of the holes in the transparent layer have different offsets from the points on the grid.  
     
     
       7. A mask according to claim  6 , wherein the three types of phase-shifting elements produce phase shifts that are offset from each other by approximately 2Π/3 radians. 
     
     
       8. A mask according to claim  6 , wherein the holes have approximately equal sizes and approximately identical shapes. 
     
     
       9. A mask according to claim  6 , wherein dimensions of the holes are between approximately one-tenth and one-twentieth of spacing between the points on the grid. 
     
     
       10. A mask according to claim  6 , wherein the phase-shifting elements are approximately rectangular in shape and are arranged in rows, wherein the three types are arranged in a repeating 123 pattern in each row, and wherein the repeating 123 patterns in each two adjacent rows are offset by approximately 1.5 phase-shifting elements. 
     
     
       11. A mask having a complex transmission function, comprising: 
       a transparent layer having three types of phase-shifting elements, each imparting a different phase shift relative to the others; and  
       a non-transparent layer having holes arranged in an approximately equally spaced grid pattern,  
       wherein the holes are approximately identical in size and overlap the three types of phase-shifting elements in different combinations.  
     
     
       12. A mask according to claim  11 , wherein the three types of phase-shifting elements produce phase shifts that are offset from each other by approximately 2Π/3 radians. 
     
     
       13. A mask according to claim  12 , wherein the three types of phase-shifting elements produce phase shifts of approximately 0, 2Π/3 radians and −2Π/3 radians, respectively. 
     
     
       14. A mask according to claim  11 , wherein the holes have approximately identical shapes. 
     
     
       15. A mask according to claim  11 , wherein the grid pattern is defined by points that are common to borders of at least three different types of phase-shifting elements. 
     
     
       16. A mask according to claim  15 , wherein dimensions of the holes are between approximately one-tenth and one-twentieth of spacing between the points that are common to borders of at least three different types of phase-shifting elements. 
     
     
       17. A mask according to claim  11 , wherein the phase-shifting elements are arranged in rows, wherein the three types are arranged in a repeating 123 pattern in each row, and wherein the repeating 123 patterns in each two adjacent rows are offset by approximately 1.5 phase-shifting elements. 
     
     
       18. A method for fabricating a mask having a complex transmission function, said method comprising: 
       obtaining a mask blank having a transparent layer that includes three types of phase-shifting elements, each imparting a different phase shift relative to the others, and also having a non-transparent layer; and  
       forming holes in the non-transparent layer so that, for each hole, the amount that said each hole overlaps each type of phase-shifting element is controlled so as to synthesize a desired complex transmission value for said each hole.  
     
     
       19. A method according to claim  18 , wherein the holes are formed in a regularly spaced grid pattern in the non-transparent layer. 
     
     
       20. A method according to claim  19 , wherein the grid pattern is defined by points that are common to borders of at least three different types of phase-shifting elements. 
     
     
       21. A method according to claim  20 , wherein dimensions of the holes are between approximately one-tenth and one-twentieth of spacing between the points that are common to the borders of at least three different types of phase-shifting elements. 
     
     
       22. A method according to claim  19 , wherein the mask is for use in patterning an integrated circuit (IC) chip and is intended to be used in conjunction with an optical system disposed between said mask and said IC chip, and wherein spacing between points in the grid pattern is not greater than approximately Π/k max , where k max  is a spatial frequency cutoff of the optical system. 
     
     
       23. A method according to claim  18 , wherein the desired complex transmission value for said each hole is synthesized by adjusting an amount of overlap of each type of phase-shifting element until            F        (       x   m     ,     y   n       )       =       ∑   k            A   mn     (   k   )                 φ   k             ,                   
       where F(x m ,y n ) is the desired complex transmission value for said each hole, A mn   (k)  is an amount of area said each hole overlaps phase-shifting element type k, and φ k  is a phase shift imparted by phase-shifting element type k. 
     
     
       24. A method according to claim  18 , wherein the three types of phase-shifting elements produce phase shifts that are offset from each other by approximately 2Π/3 radians. 
     
     
       25. A method according to claim  24 , wherein the three types of phase-shifting elements produce phase shifts of approximately 0, 2Π/3 radians and −2Π/3 radians, respectively. 
     
     
       26. A method according to claim  18 , wherein the holes have approximately identical sizes and approximately identical shapes. 
     
     
       27. A method according to claim  18 , wherein the phase-shifting elements are arranged in rows, wherein the three types are arranged in a repeating 123 pattern in each row, and wherein the repeating 123 patterns in each two adjacent rows are offset by approximately 1.5 phase-shifting elements. 
     
     
       28. A mask blank comprising: 
       a transparent layer having three types of phase-shifting elements, each imparting a different phase shift relative to the others, with the phase-shifting elements alternating in both x and y dimensions; and  
       a non-transparent layer.  
     
     
       29. A mask blank comprising: 
       a transparent layer having three types of phase-shifting elements arranged such that points common to borders of all three types form a regularly spaced grid; and  
       a non-transparent layer,  
       wherein each type of phase-shifting element imparts a different phase shift relative to the others.